Escape from Cells: Deep Kd-Networks for the Recognition of 3D Point Cloud Models

We present a new deep learning architecture (called Kd-network) that is designed for 3D model recognition tasks and works with unstructured point clouds. The new architecture performs multiplicative transformations and share parameters of these transformations according to the subdivisions of the point clouds imposed onto them by Kd-trees. Unlike the currently dominant convolutional architectures that usually require rasterization on uniform two-dimensional or three-dimensional grids, Kd-networks do not rely on such grids in any way and therefore avoid poor scaling behaviour. In a series of experiments with popular shape recognition benchmarks, Kd-networks demonstrate competitive performance in a number of shape recognition tasks such as shape classification, shape retrieval and shape part segmentation.Comment: Spotlight at ICCV'1

Learning Cooperative Games

This paper explores a PAC (probably approximately correct) learning model in cooperative games. Specifically, we are given $m$ random samples of coalitions and their values, taken from some unknown cooperative game; can we predict the values of unseen coalitions? We study the PAC learnability of several well-known classes of cooperative games, such as network flow games, threshold task games, and induced subgraph games. We also establish a novel connection between PAC learnability and core stability: for games that are efficiently learnable, it is possible to find payoff divisions that are likely to be stable using a polynomial number of samples.Comment: accepted to IJCAI 201

Geometric deep learning

The goal of these course notes is to describe the main mathematical ideas behind geometric deep learning and to provide implementation details for several applications in shape analysis and synthesis, computer vision and computer graphics. The text in the course materials is primarily based on previously published work. With these notes we gather and provide a clear picture of the key concepts and techniques that fall under the umbrella of geometric deep learning, and illustrate the applications they enable. We also aim to provide practical implementation details for the methods presented in these works, as well as suggest further readings and extensions of these ideas